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Simplifying 16t2 + -180t + 276 = 0 Reorder the terms: 276 + -180t + 16t2 = 0 Solving 276 + -180t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(69 + -45t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(69 + -45t + 4t2)' equal to zero and attempt to solve: Simplifying 69 + -45t + 4t2 = 0 Solving 69 + -45t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 17.25 + -11.25t + t2 = 0 Move the constant term to the right: Add '-17.25' to each side of the equation. 17.25 + -11.25t + -17.25 + t2 = 0 + -17.25 Reorder the terms: 17.25 + -17.25 + -11.25t + t2 = 0 + -17.25 Combine like terms: 17.25 + -17.25 = 0.00 0.00 + -11.25t + t2 = 0 + -17.25 -11.25t + t2 = 0 + -17.25 Combine like terms: 0 + -17.25 = -17.25 -11.25t + t2 = -17.25 The t term is -11.25t. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25t + 31.640625 + t2 = -17.25 + 31.640625 Reorder the terms: 31.640625 + -11.25t + t2 = -17.25 + 31.640625 Combine like terms: -17.25 + 31.640625 = 14.390625 31.640625 + -11.25t + t2 = 14.390625 Factor a perfect square on the left side: (t + -5.625)(t + -5.625) = 14.390625 Calculate the square root of the right side: 3.793497726 Break this problem into two subproblems by setting (t + -5.625) equal to 3.793497726 and -3.793497726.Subproblem 1
t + -5.625 = 3.793497726 Simplifying t + -5.625 = 3.793497726 Reorder the terms: -5.625 + t = 3.793497726 Solving -5.625 + t = 3.793497726 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + t = 3.793497726 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + t = 3.793497726 + 5.625 t = 3.793497726 + 5.625 Combine like terms: 3.793497726 + 5.625 = 9.418497726 t = 9.418497726 Simplifying t = 9.418497726Subproblem 2
t + -5.625 = -3.793497726 Simplifying t + -5.625 = -3.793497726 Reorder the terms: -5.625 + t = -3.793497726 Solving -5.625 + t = -3.793497726 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + t = -3.793497726 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + t = -3.793497726 + 5.625 t = -3.793497726 + 5.625 Combine like terms: -3.793497726 + 5.625 = 1.831502274 t = 1.831502274 Simplifying t = 1.831502274Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.418497726, 1.831502274}Solution
t = {9.418497726, 1.831502274}
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